Talk:Absorbing element

Absorbing elements for multiary operations

For a nullary operation on a set X, which is just an element x of X, all elements of X are considered to be absorbing elements, regardless of whether they are equal to x.

For a unary operation f, an absorbing element is simply a fixed point of f.

In general, an absorbing element for a multiary operation and a position i is an element x of X such that applying the operation gives x whenever the element in the ith position is x. An absorbing element is an element of X that is an absorbing element for every position. GeoffreyT2000 (talk) 02:08, 19 May 2015 (UTC)[reply]

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Further generalization

Why does the result of a product with the absorbing element have to be equal to the absorbing element? If for example $\forall s\in S$ we observe $z\cdot s=s\cdot z=w$ (or perhaps with just left or right but not both), for some $w\neq z$ , this is effectively an absorbing element too, yes? 50.35.103.217 (talk) 00:23, 15 August 2018 (UTC)[reply]

This might be a good idea. However, wikipedia requires it (per WP:OR) to be published elsewhere before it can be mentioned here. So if you find a reference, feel free to add a section here, called e.g. "Generalized absorbing elements". - Jochen Burghardt (talk) 08:36, 16 August 2018 (UTC)[reply]